Evidence reported by j.mauthe for item collectedmathem01sylvrich on Mar 16, 2006; no visible copyright symbol and date found; stated date is 1904; the country of the source library is the United States; not published by the US government.
Reviewer:a e b
March 13, 2012 Subject:
four volumes of good reading
J. J. Sylvester was an early explorer of what is now called classical invariant theory. However, the work for which he is often remembered is his theory of elimination. Given two homogenous polynomials in two variables, Sylvester eliminated the variables to find the condition that the two polynomials have a common root. He was not the first here. But he was the first to apply the approach to three homogenous polynomials in three variables, i.e. the condition that 3 plane curves intersect in a common point. He called this the 'dialytic method' of elimination. Several papers in volume 1 develop this. I have used Sylvester's papers on several occasions with problems of this nature. However, a word of warning. Frank Morley, 'The Eliminant of a Net of Curves' in the American Journal of Mathematics, 1925, had trouble using Sylvester's method in some instances, so developed another approach. However, for the applications I have had over the years, Sylvester's method has always given the correct result.
Turning to another area, Sylvester has several papers that provide the (total) number of covariants of given degree and order for a binary form of some fixed degree. This was an area of great interest in the 19th century, until Hilbert's theorems resulted in reduced interest here. Sylvester's papers are still make quite interesting reading, even though invariant theory has moved on from these types of questions.
These four volumes contain papers on many areas of mathematics, and they make very good reading.